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Question

For a two-dimensional incompressible flow field given by U =A(x^iy^j), where A>0, which one of the following statements is FALSE?
A. It satisfies continuity equation
B. It is unidirectional when x0 and y.
C. Its streamlines are given by x = y.
D. It is irrotational

A
A
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B
B
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C
C
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D
D
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Solution

The correct option is C C
C is the false statement
2D incompressible flow continuity equation.
ux+vy=0
(Ax)x+(Ay)y=0
AA=0 it satisfies continuity equation.
As U =Ax^iAy^j
where, u=Ax and v= -Ay
stream line equation for 2D

dxu=dyv

dxAx=dyAy

Inx = -In y+ In c
Inxy = In c
xy = c streamline equation
x0, Flow will be along y-axis
y0, Flow will be along x-axis

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